Long-range properties of 1S bottomonium states

In the framework of weakly coupled potential nonrelativistic QCD, we derive, first, an analytical expression for the chromopolarizability of 1S bottomonium states in agreement with previous determinations. Then we use the QCD trace anomaly to obtain the two-pion production amplitude for the chromopolarizability operator and match the result to a chiral effective field theory with 1S bottomonium states and pions as degrees of freedom. In this chiral effective field theory we compute some long-range properties of the 1S bottomonium generated by the pion coupling such as the leading chiral logarithm to the 1S bottomonium mass and the van der Waals potential between two 1S bottomonium states. Both results improve on previously known expressions.